String arrangement for musical instruments

ABSTRACT

An improved string arrangement for coupling one or more of strings to a sound radiating member, such as a soundboard, is provided having a bridge structure with a rib with a bridge face and a bearing point edge. Associated with each string and disposed at least tangent to the bearing point edge and substantially perpendicular to the bridge face is a first bridge pin. A second and/or third bridge pin may also be provided axially behind the first bridge pin for retaining each string against the bridge face. This invention provides enhanced tone quality by improving sustain and amplitude of fundamental frequencies in a convenient and simple structural arrangement for pianos and other stringed devices.

TECHNICAL FIELD

This invention relates generally to structures for stringed instruments,and more particularly, to an improved string support arrangement andbridge structure which provides increased tonal quality in theseinstruments.

BACKGROUND OF THE INVENTION

The general assembly of stringed instruments is well known in the art.For example in a piano type arrangement, a plurality of strings aretensioned across a string attachment structure, such as a plate, so thateach string may vibrate when struck by a hammer. The strings define thefrequency of the note and convert some of the kinetic energy of themoving hammer into vibrational energy with components of vibration inplanes parallel and perpendicular to the plate. Piano strings aretypically arranged either horizontally (as in a grand piano) orvertically (as in an upright piano) and are generally subdivided intothree major groupings: bass, low treble and high treble. Bass commonlyrefers to the lower-pitched notes, while treble refers to the higherpitched notes. In a piano type arrangement, there are typically threestrings for each high treble note, two strings for each low treble note,and one string for each bass note. Each set of one, two, or threestrings is often referred to as a unison. There is typically providedone key for each unison or note. A piano generally has 88 keys, andhence 88 notes, spanning at least the frequency range from the note A0at 27.5 hz to the note C8 at 4186 hz.

In a piano type arrangement, the strings engage a bridge structure fortransferring their vibrational energy to a sound amplifying structure,or soundboard. Typically, the bridge structure is disposed transverse tothe strings and comprises two angled bridge pins for each string(although some musical instruments, such as a harpsichord, typically areprovided with only one bridge pin), with both pins being attached to acurved rib having a top face. Each string has a bearing point, sometimesreferred to as a speaking, or vibrating length terminus, located at thebridge structure. Both pins were typically specified to be installed atan angle so that the strings are down-bearing against the bridge andside-bearing against the pins. Such angled bridge pins were believed tobe necessary to avoid undesirable performance characteristics, such asstrings moving off their designated bearing point at the bridgestructure when excited. In fact, inadvertent installation of pins havinginsufficient angle was to be avoided, as it could similarly cause suchperformance problems.

The down and side bearing relationship of the strings with the bridgestructure also aids in transmitting their vibrational energy to thebridge structure and, in part, defines the mechanical couplingtherebetween. Because the strings are the principal reservoir forstoring vibrational energy, it is known in the art that the magnitudeand manner of the excitation and the boundary conditions of the stringare important for determining the tone of a string, although the reasonsand interaction are often not fully understood. For example in a piano,the string is typically excited by the impact of a hammer having animpact velocity, the velocity being dependent upon the force input ofthe pianist at the piano key. It is contemplated that the impactvelocity, the physical hardness and density characteristics of thehammer (and its felt covering), and the method of coupling the string tothe bridge structure defines, in part, the initial tone of the string.

The tone of a string is often defined by the harmonic content and decaytime of the string. When a string is excited (such as by striking with ahammer), it will vibrate at a fundamental frequency which is determinedby the vibrating or speaking length of the string, the tension of thestring, and the mass per unit length of the string. The string will alsovibrate at integer multiples of the fundamental frequency, oftenreferred to as overtones, as well as frequencies producing a "glassy"sound which do not contribute to the perceived pitch of the note. Therelative strength, or amplitude, of the fundamental frequency, theovertones, and the frequencies producing the glassy sounds, oftentogether referred to as a spectrum, define the string's harmoniccontent. The larger the amplitude of the fundamental frequency and thelower overtones (e.g., generally the first 5 to 10 integer multiples ofthe fundamental frequency depending on whether the string is generallyin the high treble, low treble, or bass range), the clearer and moredesirable the tone; while alternatively, the more frequencies producingglassy sounds and the greater their amplitudes, the less desirable thetone.

In addition to the harmonic content of a string, the decay rate of theadditive amplitude of the string's excited frequencies (e.g., thefundamental frequency, the overtones, and other associated frequencies)is also important in determining a string's tonal quality. In general,the longer the decay time the more desirable the tone. It is even moredesirable that the decay time be fairly uniform from note to note sothat the multiple notes blend in pleasing harmony with each other whenplayed together. For example, in typical piano type arrangements it issometimes difficult to achieve a good balance that enables the 5thoctave and above of the keyboard (notes C5 through F6, often referred toas the melody range) to sustain long enough (i.e., having a long enoughdecay time) against the inherently longer decay time of the lower octaveranges (notes C1 through C5).

While previously available bridge structures may function well for thepurposes for which they were designed, it has often been desirable, andcontinues to be desired, to provide improved bridge structures withadditional operational advantages. For example, it would be desirable toprovide a string arrangement which increases a string's decay time sothat juxtaposed notes from different ranges in the piano sound welltogether. It would also be advantageous to provide an improved stringarrangement and bridge structure which reduces the glassy soundsassociated with a note and which also produces a clearer note. Thepresent invention provides such an improved string arrangement which canaccommodate designs having the abovedescribed tonal benefits andfeatures.

SUMMARY OF THE INVENTION

A string arrangement for musical instruments comprising at least onestring and a bridge structure for coupling the string to a soundradiating member is provided. The bridge structure is provided with abridge face and a bearing point edge. A first bridge pin is located atleast tangent to the bearing point edge and substantially perpendicularto the bridge face such that the string simultaneously contacts thebearing point edge and the first bridge pin at the bridge structure.

The bridge structure can also be provided in some preferred embodimentswith second and third bridge pins located a second pin axial distancebehind the first bridge pin and a third pin axial distance behind thesecond bridge pin, respectively. Preferably, the second and third pindistances are in a range of between about 1 mm and about 1 cm. Thesecond and third bridges pins may also be oriented, respectively, at asecond pin offset angle relative to the first bridge pin, and a thirdpin offset angle relative to the second bridge pin. In a preferredarrangement, the second and third bridge pin angles are in a range ofbetween about -45 degrees and about 45 degrees relative to the first andsecond bridge pins.

BRIEF DESCRIPTION OF THE DRAWINGS

While the specification concludes with claims particularly pointing outand distinctly claiming the invention, it is believed the same will bebetter understood from the following description taken in conjunctionwith the accompanying drawings in which:

FIG. 1 is a partial plan view of the interior of a piano arrangementmade in accordance with the present invention;

FIG. 2 is an enlarged partial plan view of a portion of the interior ofthe piano arrangement of FIG. 1;

FIG. 3 is an enlarged partial plan view of a portion of the interior ofthe grand piano of FIG. 1, illustrating an embodiment wherein a singlewire comprises two strings on a treble bridge;

FIG. 4 is a partial cross-sectional view of a portion of the soundboardof the piano arrangement of FIG. 1, taken along line 4--4 thereof;

FIG. 5 is a partial perspective view taken at a cross-section of atreble bridge structure of the piano arrangement of FIG. 1 along line5--5 thereof;

FIG. 6 is a partial cross-sectional view of a bass bridge structure ofthe piano arrangement of FIG. 1, taken along line 6--6 thereof;

FIG. 7 is an enlarged front perspective view of the treble bridgestructure of FIG. 5, looking along line of sight LS thereof;

FIG. 8 is an enlarged left side view of the treble bridge structure ofFIG. 5;

FIGS. 9A-9H are schematic views of bridge pin arrangements of thepresent invention; and

FIG. 10 is an enlarged right side view of the treble bridge structure ofFIG. 5.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference will now be made in detail to the presently preferredembodiments of the invention, examples of which are illustrated in theaccompanying drawings wherein like numerals indicate the same elementsthroughout the views. FIG. 1 is a top plan view of a portion of theinterior of an exemplary piano 20 (e.g., a grand piano) made inaccordance with the present invention, wherein the general features ofwhich will be familiar to those skilled in the art. Although thepreferred embodiments of the present invention described herein areparticularly suited for use in grand piano arrangements, it iscontemplated that the present invention may be implemented in any ofvariety of other stringed instruments such as upright pianos,harpsichords, clavichords, guitars, mandolins, violins, or the like.

Piano arrangement 20 preferably comprises a string plate 22 havingproximal end 24 and distal end 26, a plurality of strings (e.g., 28a,28b, 28c, 28d, 28e, 28f) tensioned across string plate 22, a soundboard30 adjacent the strings, and a bridge structure (e.g., 32a for treblestrings and 32b for bass strings) for coupling the strings to soundboard30. As best illustrated in FIG. 1, an exemplary high treble note isillustrated as preferably comprising strings 28a, 28b, and 28c forming afirst unison 34a, while an exemplary low treble note comprises strings28d and 28e forming a second unison 36b. An exemplary bass note is shownas preferably comprising a single string 28f forming a third unison 34c.The remaining strings of grand piano 20 have been deleted for purposesof clarity.

Each string (e.g., 28a, 28b, 28c, 28d, 28e, 28f) extends generallydiagonally across string plate 22 and is formed from a wire 40 having amechanical length (e.g., M), as best exemplified in FIG. 2. The stringis preferably mechanically terminated at proximal end 24 by tuning pin42 and at distal end 26 by hitch pin 44 and may be attached to tuningpin 42 and hitch pin 44 such as is known in the art. Although eachstring may be formed from a distinct wire 40 having a mechanical lengthM, in a more preferred arrangement, adjacent strings can be formed fromthe same wire such that mechanical length M defines both strings (FIG.3). In this arrangement which is generally referred to as "loopstringing," wire 40 is terminated at one end by first tuning pin 46a andpasses over a bridge structure (e.g., 32a or 32b as shown in FIG. 1)thereby forming first string 48a. The same wire 40 then passes aroundhitch pin 44 and over the bridge structures again where it is terminatedby second tuning pin 46b, thereby forming a second adjacent string 48b.Thus, adjacent tuning pins 46a and 46b, rather than a tuning pin andhitch pin, can define the mechanical termination points of wire 40.First string 48a and adjacent string 48b retain their own distinctivepitch because of the wire's tension and stiffness where it bends aroundhitch pin 44. Each string is preferably made of high strength steel andmay be plain or wrapped in one or more layers of covering wire or othermaterial, with each layer encircling the core in the form of amulti-turn helix.

As best seen in FIG. 4, tuning pins 42 preferably pass through stringplate 22 into pin block 50 attached to string plate 22. One end of wire40 is coiled around and attached to a tuning pin 42 so that the wire'stension may be selectively increased or decreased by turning tuning pin42 which, in turn, adjusts or "tunes" the fundamental frequency of thestring formed by wire 40. In this manner, strings forming a unison(e.g., 34a, 34b, and 34c) may be properly maintained in harmony with oneanother.

Preferably, each bridge structure is attached (such as by gluing) tosoundboard 30, so that the combined structure functions to mechanicallyoppose the downward bearing load created by the tensioned strings andalso acts as an acoustic radiating member of the stringed arrangement(e.g., piano 20) by transforming some of the mechanical energy of thestrings and bridges into acoustic energy. Soundboard 30 and bridgestructures 32a and 32b are preferably made of tone wood, either solid orlaminate. The soundboard is typically manufactured from a softwood suchas spruce while the bridge is formed from hardwoods such as maple orbeech.

As seen best in FIG. 2, the vibrational length, or speaking length, S ofeach string has a first and second terminus. The first terminus isprovided by deflection element 52 at proximal end 24 whereby asufficient deflection, or effective deflection, of the string iscreated. In a preferred arrangement, deflection element 52 can beagraffe pin 54 which is secured to string plate 22 or a V-bar (notillustrated), as is commonly known in the art.

The second terminus can be provided by a bridge structure (e.g., 32a,32b) at distal end 26, as best seen in FIGS. 5 (bridge structure 32a),and 6 (bridge structure 32b). Each bridge structure preferably comprisesa bridge rib 58 having a bridge face 60 and a first bridge pin 62a, asecond bridge pin 62b, and a third bridge pin 62c associated with eachstring. Bridge face 60 is further illustrated with a bearing point edge64 and back edge 66. As is commonly known in the art, bearing point edge64 and first bridge pin 62a preferably cooperate in defining the secondterminus of a string's speaking length S. First bridge pin 62a ispreferably located on the bridge structure (e.g., 32a or 32b) such thatat least a portion of first bridge pin 62a at least tangentiallyintersects bearing point edge 64. More preferably, first bridge pin 62ais located on the bridge structure such that bearing point edge 64approximately bisects each first bridge pin 62a, as illustrated in FIG.6, so that each string (e.g., 28a, 28b, 28c, 28d, 28e, and 28f) contactsbearing point edge 64 and first bridge pin in the same plane generallyperpendicular to the longitudinal axis of the string 62a (e.g., P), asbest illustrated in FIGS. 7 and 8. By insuring that the first bridge pincontacts or is at least tangent to the bearing edge, each string hasonly one effective second terminus of its speaking length S at thebridge structure. To insure adequate clearance between each string andthe bridge structure such that a string's first bridge structure contactis at bearing point edge 64, a first notch 68a, or cut-away, may beassociated with each unison (e.g., 34a, 34b, 34c) and disposed betweenleading edge 70 and bearing point edge 64. A second notch 68b locatedbetween trailing edge 72 and back edge 66 can also be provided so thatadequate clearance may also be provided thereat, although this notch isnot required.

First bridge pin 62a is preferably oriented in a manner substantiallyperpendicular to bridge face 60 at its attachment therewith. The termsubstantially perpendicular, as used herein, is intended to mean thatfirst bridge pin 62a has an angle A₁ (FIG. 8) relative to bridge face 60of about 90 degrees ±about 5 degrees. More preferably, angle A₁ is about90 degrees ±about 2 degrees, and most preferably is nominally about 90degrees. It is believed that placement of a first bridge pin 62a in anorientation substantially perpendicular to bridge face 60 provides atone which has a longer decay time and is "brighter" than tones ofstrings having a first bridge pin 62a which is not substantiallyperpendicular. Although the nature of the mechanical coupling betweenthe strings, bridge structures 62a and 62b and soundboard 30 and itsinfluence on tone quality is not fully understood, and not intending tobe bound by any particular theory herein, it is believed that theperceptible sustain time of an excited string in an arrangementincorporating the present invention is effectively and perceptivelylonger than a comparable string whose speaking length S is terminated bya bridge structure having a first bridge pin which is not substantiallyperpendicular, as defined herein. It is further believed that thefundamental frequency of an excited string in an arrangementincorporating the present invention may have a greater amplitude thanits first overtone when compared to a comparable string which is notsubstantially perpendicular.

It is further contemplated that the above-described benefits of asubstantially perpendicular first bridge pin are derived from anincrease in the amount of a string's initial vibrational energy in aplane generally parallel to the soundboard (i.e., generallyperpendicular to a first bridge pin incorporating the presentinvention). Because the mechanical impedance in the plane parallel tothe soundboard is high relative to the mechanical impedance in the planeperpendicular to the soundboard, a string's vibrational energy isdissipated largely in the perpendicular plane. As such, it iscontemplated that the present arrangement places more energy into aplane which is parallel to the soundboard and produces a tone with alonger decay time because more energy is initially "stored" for laterdissipation in the perpendicular plane.

The bridge structure can also be provided with a second bridge pin 62band/or third bridge pin 62c for mechanically anchoring a string suchthat it does not move off of bearing point edge 64 when excited. Secondbridge pin 62b can be preferably disposed at a second pin axial distanceD₁ behind and substantially in line with first bridge pin 62a, as bestshown in FIG. 9A where bridge structure details have been removed forclarity (FIGS. 9 A-H are intended only to illustrate possible placementsof bridge pins 62a, 62b, and 62c relative to each another, and areintended neither to be exhaustive of such arrangements nor to illustratepreferred bridge pin locations). In a more preferred arrangement,distance D₁ is in a range of between about 1 mm and about 1 cm.

Second bridge pin 62b may also be provided with a second pin offsetangle (e.g., O₁) relative to first bridge pin 62a, as best illustratedin FIGS. 9B, 9D, 9F and 9H. Offset angle O₁, as used herein, is intendedto show the angle between theoretical line T₁ parallel to wire 40 butpassing through the center point of first bridge pin 62a, andtheoretical line T₂ which passes through the center points of firstbridge pin 62a and second bridge pin 62b, as best shown in FIG. 9B.Preferably, offset angle O₁ is in a range of between about -45 degreesand about 45 degrees (FIGS. 9B through 9F depict a positive offset angleO₁ while FIG. 9H depicts a negative offset angle O₁).

Second bridge pin 62b can also be provided with a second pin orientationangle A₂ from bridge face 60, as best illustrated in FIG. 8, so thateach string is maintained in a down-bearing condition against bridgeface 60, and side-bearing against first and second bridge pins 62a and62b. In a preferred arrangement, second pin orientation angle A₂ is in arange of between about 65 degrees and about 80 degrees or in range ofbetween about 100 degrees and about 115°. It is believed that the sideand down-bearing relationship of each string may prevent movement of thestring off of bearing point edge 64 which, in turn, can prevent thesecond terminus of speaking length S from shifting when a string isexcited. In addition, maintaining the down and sidebearing condition ofeach string against bridge face 60 and first and second bridge pins 62aand 62b, respectively, can aid in the transmission of each string'svibrational energy to the bridge structure and soundboard 30. Althoughit is preferable that second bridge pin 62b be oriented at an angle A₂,it is contemplated that it can also be substantially perpendicular tobridge face 60, and may further be provided with a notch, groove, or thelike (not illustrated) for restricting movement of a string (e.g., 28a,28b, 28c, 28d, 28e, 28f) in a direction generally perpendicular tobridge face 60.

Third bridge pin 62c can preferably be located at a third pin axialdistance D₂ behind and substantially in line with second bridge pin 62b,as best seen in FIG. 9C. Although it is believed that the exact locationof third bridge pin 62c is not critical, in a more preferredarrangement, third bridge pin 62c is placed at a distance D₂ in a rangeof between about 1 mm and about 1 cm at pin 62b. Third bridge pin 62ccan be oriented substantially perpendicularly to bridge face 60, or maybe preferably provided at a third pin orientation angle A₃ (FIG. 10)with respect to bridge face 60 with such angle being in a range ofbetween about 65 degrees and about 80 degrees if it is located on thesame side of the string as second bridge pin 62b (FIG. 2).Alternatively, third bridge pin 62c may preferably be provided with athird pin orientation angle A₃ in a range of between about 100 degreesand about 115 degrees if it is located on the opposite side of thestring as second bridge pin 62b (e.g., FIG. 9G).

In a more preferred arrangement, third bridge pin 62c may be providedwith a third pin offset angle O₂ from second bridge pin 62c. Offsetangle O, as used herein, is to connote the angle between theoreticalline T₃, which is parallel to or colinear with theoretical line T₁, andtheoretical line T₄ which passes through the center points of secondbridge pin 62b and third bridge pin 62c, as best seen in FIG. 9E.Preferably, offset angle O₂ is in a range of between about -45 degreesand about 45 degrees (FIGS. 9D, 9E and 9F depict a positive offset angleO₂ while FIG. 9H depicts a negative offset angle O₂).

Although it is preferred that bridge structure 32a or 32b be providedwith three bridge pins per string, it is contemplated that the bridgestructures may be provided with various other pin arrangements, such aswith only two bridge pins (i.e., a first substantially perpendicularbridge pin 62a and second bridge pin 62b), without deviating from thescope of this invention. Similarly, it is also contemplated that thebridge structures may be provided with only a single substantiallyperpendicular first bridge pin 62a with each string being anchored by apin, or other anchoring structure, at some axial distance behind thebridge structure (not illustrated). In the alternative, a single bridgepin (not illustrated) may be provided which combines the functions andstructure of first bridge pin 62a with second bridge pin 62b (notillustrated). Such a single bridge pin, for example, could be providedwith both a substantially perpendicular face and an angled face asotherwise provided herein by separate bridge pins.

The bridge pins may be manufactured from hardened steel, or the like,and may hollow, or more preferably solid, and coated with copper, chromeor zinc for wear resistance. Although it is believed that the diameterof the bridge pins may vary without detracting from the scope of thisinvention for use in piano arrangements, it is preferred that the eachpin have a diameter in range of between about 0.15 cm and about 0.25 cm.In addition, although it is preferred that each bridge pin have asubstantially cylindrical shape, it is contemplated that otherconformations (e.g., elliptical or otherwise rounded, square,triangular) and configurations (e.g., a single pin combining thefunction and/or structure of first bridge pin 62a, second bridge pin62b, and/or third bridge pin 62c) may be equally suitable.

The foregoing description of the preferred embodiments have beenpresented for purposes of illustration and description, and is notintended to be exhaustive or to limit the invention to the precise formsdisclosed. Modifications or variations are possible and contemplated inlight of the above teachings by those skilled in the art, and theembodiments discussed were chosen and described in order to bestillustrate the principles of the invention and its practicalapplication, and indeed to thereby enable utilization of the inventionin various embodiments and with various modifications as suited to theparticular instrument and use contemplated. It is intended that thescope of the invention be defined by the claims appended hereto.

We claim:
 1. A string arrangement for musical instruments having at least one string coupled to a sound radiating member, said arrangement comprising:a bridge structure having a bridge face and a bearing point edge; a first pin located adjacent to said bearing point edge and substantially perpendicular to said bridge face; a second pin located at a second pin distance behind said first pin; and a string contacting said first and second pins, said second pin maintaining said string in down-bearing contacting relation with said bearing point edge.
 2. The string arrangement of claim 1, wherein said second pin is located axially behind said first pin.
 3. The string arrangement of claim 1, wherein said second pin is oriented at a second pin offset angle relative to said first bridge pin.
 4. The string arrangement of claim 1, further comprising a third bridge pin located at a third pin axial distance behind said second pin.
 5. The string arrangement of claim 4, wherein said third pin has a third pin offset angle from said second bridge pin.
 6. The string arrangement of claim 1, further comprising a plurality of strings.
 7. The string arrangement of claim 1, wherein said second pin is disposed on said bridge structure.
 8. A string arrangement for musical instruments comprising:a string plate; a plurality of strings tensioned across said plate; a soundboard located adjacent said string plate; a bridge structure attached to said soundboard for coupling said strings to said soundboard, said bridge structure having a bridge face and a bearing point edge; a first bridge pin associated with each of said strings and located at least tangent to said bearing point edge and substantially perpendicular to said bridge face, each of said strings contacting said bearing point edge and its associated first pin; and a second bridge pin associated with each of said first bridge pins and located at a second pin distance behind said first bridge, said second bridge pin maintaining its associated string in down-bearing contacting relation with said bearing point edge.
 9. The string arrangement of claim 8, wherein said second pin distance is in a range of from 1 mm to 1 cm from said first pin.
 10. The string arrangement of claim 8, wherein said second pin is oriented at a second pin offset angle relative to said first bridge pin.
 11. The string arrangement of claim 10, wherein said second pin offset angle is in a range of from -45 degrees to 45 degrees.
 12. The string arrangement of claim 8, wherein said second pin is oriented at a second pin orientation angle.
 13. The string arrangement of claim 12, wherein said second pin orientation angle is in a range of from 65 degrees to 80 degrees from said bridge face.
 14. The string arrangement of claim 8 further comprising a third bridge pin located a third bridge pin distance axially behind said second pin.
 15. The instrument of claim 14, wherein said third pin distance is in a range of from 1 mm to 1 cm from said second pin.
 16. The instrument of claim 14, wherein said third pin is oriented at a third pin orientation angle.
 17. The instrument of claim 14, wherein said third pin is oriented at a third pin offset angle relative to said second pin.
 18. The instrument of claim 15, wherein said third pin offset angle is in a range of from -45 degrees to 45 degrees.
 19. A string arrangement for musical instruments comprising:a string plate having a proximal end; a plurality of strings tensioned across said plate, each said string having a vibrational length; a deflection element associated with each said string disposed adjacent said proximal end, said deflection element providing a first terminus of said vibrational length of each said string; a soundboard located adjacent said string plate; a bridge structure attached to said soundboard for coupling said strings to said soundboard, said bridge structure having a bridge face and a bearing point edge; a first bridge pin associated with each of said strings and located at least tangent to said bearing point edge and substantially perpendicular to said bridge face, each of said strings contacting said bearing point edges said first pin providing a second terminus of said vibrational length of its associated string; and a second bridge pin associated with each of said first bridge pins and located at a second pin distance behind said first bridge pin, said second bridge pin maintaining its associated string in down-bearing contacting relation with said bearing point edge.
 20. The string arrangement of claim 19, wherein said deflection element is an agraffe pin.
 21. The string arrangement of claim 19, wherein said second pin is oriented at a second pin offset angle relative to said first pin. 